Question: $g(x)=9+\dfrac{5}{4}x$ $h(x)=10x-28$ Write $(g\circ h)(x)$ as an expression in terms of $x$. $(g\circ h)(x)=$
Solution: First, let's write $(g\circ h)(x)$ as $g(h(x))$ Next, we write $h(x)$ as the input to function $g$. $g({h(x)})=9+\dfrac{5}{4}\left({h(x)}\right)$ Since $h(x)=10x-28$, this becomes: $\begin{aligned} g({h(x)})&=9+\dfrac{5}{4}\left({10x-28}\right)\\ \\ &=9+12.5x-35\\ \\ &=12.5x-26\\ \\ \end{aligned}$ Note: We simplified the result to obtain a nicer expression, but this is not necessary. The answer: $(g\circ h)(x)=12.5x-26$